Spiking Neural Operators for Scientific Machine Learning

Abstract

One of the main broad applications of deep learning is function regression. However, despite their demonstrated accuracy and robustness, modern neural network architectures require heavy computational resources to train. One method to mitigate or even resolve this inefficiency has been to draw further inspiration from the brain and reformulate the learning process in a more biologicallyplausible way, developing what are known as Spiking Neural Networks (SNNs), which have been gaining traction in recent years. In this paper we present an SNN-based method to perform regression, which has been a challenge due to the inherent difficulty in representing a function's input domain and continuous output values as spikes. We use a DeepONet -neural network designed to learn operators -to learn the behavior of spikes. Then, we use this approach to do function regression. We propose several methods to use a DeepONet in the spiking framework, and present accuracy and training time for different benchmarks.